Spatially-coupled low-density parity check (LDPC) codes have been developed based on a method for constructing an LPDC convolutional code. Specifically, the spatially-coupled LDPC code is defined by a spatially-coupled protograph. The spatially-coupled protograph is formed by coupling protographs for a plurality of regular LDPC codes. The performance limit of the spatially-coupled LDPC code during iterative decoding (that is, belief propagation [BP] decoding) reaches the maximum likelihood decoding performance of a regular LDPC code that forms the corresponding spatially-coupled protograph. Here, the maximum likelihood decoding performance of the regular LDPC code asymptotically approaches a Shannon limit (that is, a theoretical limit) with increasing the degree of the corresponding check node (that is, a row weight on the corresponding parity check matrix). Namely, the iterative decoding performance of the spatially-coupled LDPC code based on the regular LDPC code with the check node degree being set to a very large value can be made to asymptotically approach the Shannon limit. On the other hand, the computational complexity per iteration during iterative decoding is generally proportional to the check node degree. Hence, the computational complexity significantly increases when the iterative decoding performance of the spatially-coupled LDPC code is made to asymptotically approach the Shannon limit.
Furthermore, Mackay-Neal (MN) codes and Hsu-Anastasopoulos (HA) codes are expected to have their maximum likelihood performance asymptotically approach the Shannon limit. For spatially-coupled MN codes and spatially-coupled HA codes based on the MN codes and HA codes, the iterative decoding performance on a binary erasure channel has been numerically demonstrated to asymptotically approach the Shannon limit. Here, the check node degree for the MN code and the HA code is given as a constant. The constant is smaller than the check node degree that is set to make the maximum likelihood decoding performance of the regular LDPC code asymptotically approach the Shannon limit. Hence, compared to the above-described spatially-coupled LDPC code based on the regular LDPC code, the spatially-coupled MN code and the spatially-coupled HA code enable a reduction in the computational complexity if the iterative decoding performance is made to asymptotically approach the Shannon limit. However, both the spatially-coupled MN code and the spatially-coupled HA code are non-systematic codes, a data bit sequence cannot be taken out from a codeword bit sequence unless a decoding process is carried out on these codes.